The ratio of the mass of a nitrogen atom to the mass of an atom of 12 C is 7:6, and the ratio of the mass of nitrogen to oxygen in N 2 O is 7:4. Find the mass of 1 mol of oxygen atoms.

Hello everyone. Today's the question asks, Silicon di sulfide is a promising new material for the production of Catholics in solid state batteries. The mass ratio of silicon, sulfur and silicon di sulfide is 7 to 8 while the ratio of masses between the sulfur atom and the carbon 12 atom is 8 to 3. What is the mass of one mole of silicon atoms? So first we need to note the ratio between sulfur and carbon 12. The ratio between sulfur and carbon 12 estimated in the question Is 8.3. Or in other words we can say this is also going to be equal 16-6. We just multiply two to each compound. So we then find the ratio of silicon to sulfur. Ask We know that this should be seven 2 simply because we have seven silicon from the question stem And for sulfur we have 16 on the left bare. This ultimately means So thus three show of carbon 12 to silicon is now six 27. Now we must find the mass of one mole of silicon atoms and that is going to be equal to first we're going to take one atom, one Carbon 12 Atom. We're gonna place that over one sulfur atom. We're gonna multiply by avocados number which is 6.02 times 10 to the 23rd power and say that those atoms there is equal to one mole of sulfur. We are then multiply that buy avocados number but this time on the denominator. Never gonna say this is in terms of our carbon 12. So one mole of carbon 12 is equal to 6.2 times 10 to the 23rd atoms of carbon. We're then going to bring this equation down here. We're going to multiply that number By the multiple ratio by saying two moles of Sulfur equal one mole of Silicon. As we see in this equation in the question stem almost done here, are they going to multiply that ratio by the molar mass of carbon 12. So 12 g of carbon 12 equals one mole Of carbon 12. And lastly, we're going to multiply by our ratio of silicon to sulfur or carbon. So we have seven g of silicon to six g of carbon 12. And so our units are all going to cancel out, cancel those. We can cancel these, we can cancel these and essentially, you want to be left with grams of silicon over moles of silicon. So this is going to be equal to 28 g of silicon over one mole of silicon. As our final answer. I hope this helped handle next time

Ch.2 - Atoms & Elements

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Ch.2 - Atoms & Elements

Problem 98

Chapter 2, Problem 98

The ratio of the mass of a nitrogen atom to the mass of an atom of ¹²C is 7:6, and the ratio of the mass of nitrogen to oxygen in N₂O is 7:4. Find the mass of 1 mol of oxygen atoms.

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First, we need to understand that the mass of an atom of 12C (carbon-12) is exactly 12 atomic mass units (amu) by definition. Given that the ratio of the mass of a nitrogen atom to the mass of an atom of 12C is 7:6, we can set up a proportion to find the mass of a nitrogen atom. Let's denote the mass of a nitrogen atom as 'N'. So, we have N/12 = 7/6.

Next, solve the proportion for 'N' to find the mass of a nitrogen atom in atomic mass units (amu).

Then, we know that the ratio of the mass of nitrogen to oxygen in N2O is 7:4. This means that for every 7 parts of nitrogen, there are 4 parts of oxygen. Since there are two nitrogen atoms in N2O, the mass of one nitrogen atom is half of the total nitrogen mass in N2O. So, we can set up another proportion: (N/2) / O = 7/4, where 'O' is the mass of an oxygen atom.

Solve this proportion for 'O' to find the mass of an oxygen atom in atomic mass units (amu).

Finally, to find the mass of 1 mol of oxygen atoms, multiply the mass of an oxygen atom (in amu) by Avogadro's number (6.022 x 10^23). This is because 1 mole of any substance contains Avogadro's number of particles (atoms, in this case).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atomic Mass and Molar Mass

Atomic mass is the mass of an individual atom, typically measured in atomic mass units (amu). Molar mass, on the other hand, is the mass of one mole of a substance, expressed in grams per mole (g/mol). Understanding these concepts is crucial for converting between the mass of atoms and the mass of moles, which is essential for solving stoichiometric problems.

Mass Ratios in Compounds

Mass ratios in compounds indicate the relative masses of different elements within a compound. In the question, the mass ratio of nitrogen to oxygen in N2O is given as 7:4, which allows us to set up a relationship between the masses of nitrogen and oxygen. This concept is fundamental for determining the mass of one mole of oxygen based on the provided ratios.

Stoichiometry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves using ratios derived from balanced chemical equations to calculate the amounts of substances involved. In this question, stoichiometry is applied to find the mass of oxygen based on the mass ratios provided for nitrogen and oxygen.